Electrochemistry

1. Electrochemistry (Introduction)

2. 1. Review of equilibrium electrochemistry
Electrochemical potentials and electrochemical equilibrium
Cell potentials and electrochemical series
(NHE and absolute EMF scale)
Nernst equation, Activities of ions in solutions and formal potentials
Conductivities of electrolytes
2. Dynamic electrochemistry – Electrodics
Electrode – electrolyte Interface
Factors determining electrochemical reaction kinetics
(Mass transfer, electron transfer)
Reference electrodes
Voltammetric techniques
Elucidation of reaction mechanisms
3. Application of electrochemical principles
Electrochemical analysis, electrochemical sensors
Fuel cells and batteries

3. Zn + Cu2+  Zn2+ + Cu Spontaneous rx
Electrochemical reactions
What is the amount of energy released
(under const. T and P) ?

4. Zn + Cu2+  Zn2+ + Cu Spontaneous rx
Go = -212.6 kJ/mol
Electrochemical reactions

5. Eo = -0.76 vs SHE
Eo = +0.34 vs SHE
Ecell = Ecathode - Eanode

6. Electrochemistry (introduction)
a. Origin of electrode potentials
b. Electrochemistry and thermodynamics
c. Conventions in cell representation
d. Reference electrodes
e. Electrode and formal potentials

7. Bonding in Metals
• The electron-sea model is a simple depiction of a
metal as an array of positive ions surrounded by
delocalized valence electrons.
- A metal also conducts heat well because the mobile
electrons can carry additional kinetic energy
- Metals are good conductors of electricity because
of the mobility of these delocalized valence electrons.
- Molecular orbital theory gives a more detailed picture of the
bonding in metals.
- Energy levels crowd together into bands  called as band
theory.

8. Lithium according to Band Theory
Conduction band:
empty 2 s antibonding
Valence band:
full 2 s bonding

9. Sodium According to Band Theory
Conduction band:
empty 3s antibonding
Valence band:
full 3s bonding
No gap
1s, 2s & 2p bands completely filled

10. Magnesium metal
3s band would be full
1s, 2s & 2p bands would be full
3s & 3p bands overlap

11. Sodium According to Band Theory

12. Overlap of atomic orbitals in a solid gives rise
to the formation of bands separated by gaps.
E << kT
~ 0.025 eV
Bonding in Metals

13. Band Structure

14. The Fermi level
At T > 0 K states above EF are also
occupied to a certain extent.
The population P is given by the
Fermi Dirac statistics (takes into
account that no more than two
electrons can occupy any level).
Fermi energy level

15. Fermi Level
E=0 (vacuum level)
EF (Fermi level)
Minimum energy required
to remove electron from
sample
 Each material’s energy state distribution is unique;
EF is different for different metals..
Metal 1 Metal 2
EF (Fermi level)
The closer an electron is to the vacuum
level, the weaker it is bound to the solid.
or, the more energetic is the electron.
Work
function of
metal 1

16. Two Conductors in Contact
Electron flow leads to charge
separation  Contact potential
– +
– +
– +
– +
– +
Fermi level
the same
throughout
sample
– +

17. An Ion in Solution
 Ion’s electronic structure in solution: HOMO, LUMO, HOMO-LUMO gap.
Lowest Unoccupied
Molecular Orbital
Highest Occupied
Molecular Orbital
HOMO-LUMO
Gap
“Fermi” level
EF (Fermi level)
higher or lower
than of ion in
solution
Metal

18. Metal in an Electrolyte Solution
Charge is transferred to equilibrate Fermi levels, producing a charge separation
and a contact potential difference.
Fermi levels
are aligned
+ –
+ –
+ –
Two Electrolyte Solutions
“Fermi” level
+ –
+ –
+ –

19. Zn - Zn2+
equilibrium
+ –
+ –
+ –
+ –
+ –
+ –
Fermi levels
are aligned
Fermi levels
are aligned
Potential difference
between electrodes
Cu - Cu2+
equilibrium

20. Electrochemical Thermodynamics
Every substance in a system contributes to its energy:
Chemical Potential,  (= o + RT ln a)
When the substance is a charged particle (such as an electron or an ion), the response of the
particle to an electrical field in addition to its Chemical Potential needs to be included:
Electrochemical Potential.
 =  + z F f
Chemical potential (or electrochemical
potential if it is charged) is the measure of
how all the thermodynamic properties
vary when we change the amount of the
material present in the system.
 =
G
n



T,P
Formally we
can write

21. Electrode potentials



 ne
M
s
M n
1
1 )
(
When a piece of a metal (M1) is immersed in an aqueous
solution, the following equilibrium is established:
M
Mz+
ze
-
Potential
difference
between
solution and
metal 1
M1
M1
n+
ne
-
 =  + z F f
)
(
)
( 1
1 M
M 
 =


22. Electrode potentials



 ne
M
s
M n
2
2 )
(
When a piece of a metal (M2) is immersed in an aqueous
solution, the following equilibrium is established: M2
M2
n+
ne
-
Potential
difference
between
solution and
metal 2
)
(
)
( 2
2 M
M 
 =


23. Cell emf and overall
reaction Gibbs energy:
)
( 1
2 f
f 




= F
n
Grx When the cell is balanced against an external source of
potential, the system is under equilibrium.
)
( 1
2 f
f 



=
 F
n
Grx
)
( 1
2 E
E
F
n
Grx 

=
 Nernst Equation is at the heart of electrochemistry. It identifies
the amount of work we can extract electrically from a system.

24. Chemical Reaction in
a Daniel Cell
Zn
Cu
Cu
Zn
rx
G 


 


=
 
 2
2
       
2 2
Zn s Cu aq Zn aq Cu s
 
  
Zn
Zn2+
e
-
Cu
Cu2+
e
-
Salt Bridge
1.10
V





 

=


=

2
2
2
2
2
2 ln
ln
Cu
Zn
o
rx
Cu
Zn
o
Cu
o
Zn
rx
a
a
RT
G
a
a
RT
G 

When elements and ions are at their
standard state
(i.e. pure elements at 1 bar and at
temperature T and ions at unit activity)
0 0
2
Zn
Cu
G FE
 = 
2
2
0
ln Zn
Cu
a
RT
E E
nF a


= 
2
a
ln
RT
μ
μ
since O

=

25. Electrode Convention
A cell operating spontaneously in this configuration is
said to have a positive total cell potential.
The electrode where oxidation occurs is anode.
The electrode where reduction occurs is cathode.
 When connecting a voltmeter, we connect the
positive terminal to the electrode (assumed)
positive .
 If it reads a + ve potential, correct identification of
all terminals made.
 If a – ve potential is read, then misidentification
of the reactions in the cells made.
 Reverse our assignment of anode and cathode.
In a galvanic cell the cathode is + ve and in an electrolytic cell the cathode is – ve.
Anode represented on the left and the cathode on the right.

26. Shorthand notation
Zn | Zn2+ (___M) || Cu2+(___M) | Cu
anode cathode
Phase boundary with junction
potential
No liquid junction potential
(e.g., salt bridge)
Other examples:
Pt | H2(g) (a=1) | H+ (a = 1) || Cu2+(0.01M) | Cu
Pt | Fe2+(0.001M) || KCl (sat’d) | Hg2Cl2 | Hg
Zn + Cu2+  Zn2+ + Cu
 Write components in sequence
 Separate phases with a single vertical line “|”
 A salt bridge or membrane is represented by a double vertical line “||”
 Included a specification of the species concentration

27. Is it possible to measure the potential of the
individual electrodes (i.e. potential difference
between an electrode and the solution) ?
NO!
Introducing one more electrode in solution
brings in another metal-solution interface !
Standard Reference Electrode
Measurement against a standard reference electrode.
M2
M2
n+
ne
-

28. Standard Hydrogen Electrode
The standard potential of the SHE is arbitrarily assigned a value of 0 V.

29. Standard Reduction Potentials
In a galvanic cell the cathode is the
positive electrode while the anode
is the negative electrode.
Connect Cu electrode to
positive terminal and SHE to
negative terminal of voltmeter

31. Unfortunately, single ion activities
can’t be measured…
)
m
.
(m
ln
RT
μ
ν
μ
ν
)
a
.
(a
ln
RT
μ
ν
μ
ν
a
ln
RT
μ
ν
a
ln
RT
μ
ν
μ
)
a
ln
RT
(μ
ν
)
a
ln
RT
(μ
ν
μ
a
ln
RT
μ
μ
A
ν
M
ν
yield
to
solvent
a
in
dissolves
A
M
ν
ν
ν
ν
o
o
ν
ν
o
o
ν
o
ν
o
o
o
o
Z
Z
ν
ν
-
-








































=


=



=



=

=



This defines a
mean activity
for the salt












=
=
=








where
a
a
a
activity
ionic
Mean
a
a
a
1
)
.
(
.

32. )
a
.
(a
ln
RT
μ
ν
μ
ν
a
ln
RT
μ
ν
a
ln
RT
μ
ν
μ
)
a
ln
RT
(μ
ν
)
a
ln
RT
(μ
ν
μ
a
ln
RT
μ
μ
A
ν
M
ν
yield
to
solvent
a
in
dissolves
A
M
ν
ν
o
o
ν
o
ν
o
o
o
o
Z
Z
ν
ν
-
-




























=



=



=

=

This defines a mean
activity for the salt
)
.
(
ln
2
ln
2
ln
)
ln
(
2
)
ln
(
ln
Cl
2
Ca
CaCl
2
2
-
2
2
2
2
2
2
2
2
2
2
2
2
2
-














=



=



=

=


Cl
Ca
o
Cl
o
Ca
Cl
o
Cl
Ca
o
Ca
CaCl
Cl
o
Cl
Ca
o
Ca
CaCl
CaCl
o
CaCl
CaCl
a
a
RT
a
RT
a
RT
a
RT
a
RT
a
RT
ions
yield
to
solvent
a
in
dissolves










3
1
2
2
)
.
(
.
2
2
2
2




=
=
 Cl
Ca
CaCl
Cl
Ca
CaCl
a
a
a
activity
ionic
Mean
a
a
a












=
=
=








where
a
a
a
activity
ionic
Mean
a
a
a
1
)
.
(
.

33. Mean Ionic Activity Coefficients
This defines a mean ionic activity coefficient















1
1
1
)]
.
(
.
)
.
[(
]
)
.
(
.
)
.
[(
)
.
(



















=
=
=
m
m
m
m
a
a
a
2
2
2
2
2
2
2
2
2
.
)]
.
(
.
)
.
[(
]
)
.
(
.
)
.
[(
)
.
(
3
1
2
2
3
1
2
3
1
2
CaCl
CaCl
CaCl
Cl
Ca
Cl
Ca
Cl
Cl
Ca
Ca
Cl
Ca
CaCl
m
a
m
m
m
m
a
a
a




=
=
=
=























=
=






where
a
a
a
1
)
.
(













=
=
=
m
a
m
m
m
.
)
.
(
)
.
(
1
1










m
m
a
m
m
a










=
=
=
=






.
.
.
.
m
m
and
m
m 


 =
= 


34. Mean ionic concentration
Activity of the electrolyte = (a) = (  m )
for CaCl2 it is 41/3m,
for CuSO4 it is m,
and LaCl3 it is 271/4m.
Activity of cation = a+ =  m+
Activity of anion = a- =  m-
 
  m
m
m
m
m
m
m
.
)
(
.
)
(
)
(
.
)
(
)
.
(
1
1
1



























=
=
=
m
m
m
m
m Cl
Na
NaCl
=
=
= 


2
1
2
2
1
)
(
)
.
(
m
m
and
m
m 


 =
= 

NaCl

35. ci is the conc. of i in mol/kg and
zi is the charge of the species
Mean Activity Coefficients
A  1/(RT)3/2
Log ± = -0.509 m1/2 + b m

37. aH+ =  mH+
0 1 2 3 4 5
0
2
4
6
8
10
12
Activity
of
H
+
Molality of HCl

38. 
=
i
i
i Z
C 2
5
.
0
I
Ci = molal con.
of ions
I = ionic strength
of solution
a±(HCl) = 1
1.18 M
Actual conc of
solution is very
high. Water of
solvation has
reduced free
water molecules
a = m 

39. Determination of Eo

40. 1/2H2(g) + AgCl(s)  HCl(aq) + Ag(s)
2
/
1
)
(
ln
2
H
HCl
O
P
a
F
RT
E
E 
=
Assuming H2(g) to be ideal and with PH2 = 1 bar:



=


=


log
303
.
2
*
2
log
303
.
2
*
2
)
.
(
log
303
.
2 2
F
T
R
E
m
F
T
R
E
m
F
T
R
E
E
o
o
At infinite dilution, m = 0,  = 1. log  = 0.
m+ = m = m for HCl solution












=
=
=








where
a
a
a
a
a
a
1
)
.
(
.
















=
=
=
=
m
a
m
a
m
m
m
t
coefficien
activity
ionic
Mean
.
.
)
.
(
)
.
(
1
1












41. m
vs
m
F
T
R
E
of
Plot )
log
303
.
2
*
2
( 
Extrapolation of this plot to m = 0 will
give Eo
E of Ag(s) | AgCl(s), HCl (a = 1), i.e.
Eo of the half cell is measured.
Eo is known (= 0.224V at 25oC) and hence
from emf of the cell (E) at diff. conc. of HCl
(m),  can be obtained.


=
 
log
303
.
2
*
2
log
303
.
2
*
2
F
T
R
E
m
F
T
R
E o

42. For 1-1 electrolyte, an at 25oC:
Log ± = -0.509 m1/2
Extended Debye-Huckel law for 1-1
electrolyte:
Log ± = -0.509 m1/2 + b m
b = constant


=
 
log
303
.
2
*
2
log
303
.
2
*
2
F
T
R
E
m
F
T
R
E o
E of Ag(s) | AgCl(s), HCl (a. = 1), i.e.
Eo of the half cell is measured.
Substitute into eqn above and rearrange:
E + 0.1183 log m – 0.0602 m1/2 = E’ = Eo – (0.1183b) m
Plot E’ vs m. intercept is Eo.

43. Standard Electrode Potentials
Standard electrode potential is the potential of the cell with hydrogen
electrode is on the left and all components of the cell are at unit activity.
Pt | H2(g) (a=1) | H+ (a=1) || Cu2+(a=1) | Cu













2
3
2
2
2
2
Fe
e
Fe
Cu
e
Cu
Zn
e
Zn
ALWAYS written as
reduction reactions
V
E
H
e
H o
000
.
0
2
2 2 =

 

Eo value is indication of
driving force for reduction.
Eo is a constant !
V
E
Cu
e
Cu o
339
.
0
2
2
=

 

Eo assumes unit activity
for all species!

44. Standard Potential Tables
All of the equilibrium electrochemical data is cast in
Standard Reduction Potential tables.
F2 + 2e–  2F– +2.87
Co3+ + e–  Co2+ +1.81
Au+ + e–  Au +1.69
Ce4+ + e–  Ce3+ +1.61
Br2 + 2e–  2Br– +1.09
Ag+ + e–  Ag +0.80
Cu2+ + 2e–  Cu +0.34
AgCl + e–  Ag + Cl– +0.22
Sn4+ + 2e–  Sn2+ +0.15
2H+ + 2e–  H2 0.0000
Pb2+ + 2e–  Pb -0.13
Sn2+ + 2e–  Sn -0.14
In3+ + 3e–  In -0.34
Fe2+ + 2e–  Fe -0.44
Zn2+ + 2e–  Zn -0.76
V2+ + 2e–  V -1.19
Cs+ + e–  Cs -2.92
Li+ + e–  Li -3.05
Reducing
power
increases
Oxidising
power
increases

45. Using the Tables
 Choose one reaction for reduction
F2 + 2e–  2F– +2.87
Co3+ + e–  Co2+ +1.81
Au+ + e–  Au +1.69
Ce4+ + e–  Ce3+ +1.61
Br2 + 2e–  2Br– +1.09
Ag+ + e–  Ag +0.80
Cu2+ + 2e–  Cu +0.34
AgCl + e–  Ag + Cl– +0.22
Sn4+ + 2e–  Sn2+ +0.15
Overall Reaction:
2Au+ + Cu  Cu2+ + 2Au
Au+ + e–  Au
Cu  Cu2+ + 2e–
Cell potential E:
E = +1.69 - 0.34 = +1.35 V
 Choose one reaction for oxidation
Ecell = Ecathode - Eanode
Cu| Cu2+ (a=1) || Au+ (a=1) | Au
anode cathode

46. Using the Tables
 Choose one reaction for reduction
F2 + 2e–  2F– +2.87
Co3+ + e–  Co2+ +1.81
Au+ + e–  Au +1.69
Ce4+ + e–  Ce3+ +1.61
Br2 + 2e–  2Br– +1.09
Ag+ + e–  Ag +0.80
Cu2+ + 2e–  Cu +0.34
AgCl + e–  Ag + Cl– +0.22
Sn4+ + 2e–  Sn2+ +0.15
 Choose one reaction for oxidation
Ecell = Ecathode - Eanode
Sn4+ + 2e–  Sn2+
Ce3+  Ce4+ + e–
Overall Reaction:
Sn4+ + 2Ce3+  Sn 2+ + 2Ce4+
Cell potential E:
E = +0.15 - 1.61 = -1.46 V
Pt | Ce3+ (a=1), Ce4+ (a=1) || Sn4+ (a=1), Sn2+ (a=1), Pt
anode cathode

47. Formal Potentials
 Standard states are impossible to achieve
(Electrochemical investigations/processes are always in
excess of inert electrolyte)
 Theoretical calculations of mean activity coefficients
possible only below 10-2 M.
 Formal potential is that for the half-cell when the
concentration quotient in the Nernst equation
equals 1 (solutions of same ionic strength with
identical inert electrolytes)
 Solution with a high concentration of inert electrolyte,
activity coefficients are constant. Use formal potentials
which are appropriate for that medium and molar
concentrations for very accurate work.
 Often specified as occurring in 1.0 M HClO4, 1.0
M HCl, or 1.0 M H2SO4.
2
2
0
ln Zn
Cu
a
RT
E E
nF a


= 

48. Example
Consider the Fe(III)/Fe(II) couple. The Nernst equation reads
When the concentration quotient is 1, the last term is 0.
This defines the new formal potential as
In a solution with excess of inert electrolyte, because the activity
coefficients are constant, this new reference potential is constant.
E = EFe3 /Fe2 
RT
F
ln
aFe2
a
Fe3





= EFe3 /Fe2 
RT
F
ln
 Fe2 Fe2
 

Fe
3 Fe3
 








= EFe3 /Fe2 
RT
F
ln
 Fe2

Fe3






RT
F
ln
Fe2
 
Fe3
 








E
'
= EFe3 / Fe2 
RT
F
ln
 Fe2

Fe
3







49. Example continued
The standard reduction potential for the Fe(III)/Fe(II) couple is
E° = 0.771 V
In 1.0 M HClO4: E°’(1.0 M HClO4) = 0.732 V
In 1.0 M HCl E°’(1.0 M HCl) = 0.700 V

50. Reference electrodes
• SHE not very practical as reference
• Prefer a half cell that is stable and
easily made to produce same Eo
V
E
Cl
Hg
e
Cl
Hg
V
E
KCl
m
Cl
Hg
e
Cl
Hg
242
.
0
KCl)
d
(sat'
2
2
2
334
.
0
)
1
.
0
(
2
2
2
'
0
2
2
0
2
2

=




=







Example:
Hg2Cl2(s) | Hg(l) | KCl (sat’d) “Saturated calomel electrode” (SCE)
V
E
Cl
Ag
e
AgCl
V
E
KCl
m
Cl
Ag
e
AgCl
222
.
0
KCl)
d
(sat'
197
.
0
)
1
.
0
(
'
0
0

=




=







AgCl(s) | Ag(s) | KCl (sat’d) “Silver-silver chloride electrode”

51. SCE Ref electrode
0.242 V vs NHE at 25oC

52. Ag/AgCl Ref electrode
0.222 V vs NHE at 25oC

54. Absolute potentials

55. Absolute electrode potentials
Pt / H2(g), H+ (a =1)
Half cell reaction: ½ H2(g)  H+ (a = 1) + e-
½ H2 (g) H+ + e-
H(g)
H+ ( a = 1) aq. + Pt
G(atomisation) G(Ionisation)
G(solvation) Work function
G = - n FE
Absolute electrode potential of Pt / H2(g), HCl (a = 1) = 4.5 V

56. Relationship between potentials on
the NHE, SCE, and "absolute" scales

58. Instrumental Methods of
Analysis: Willard, Dean and
Meritt